Regularity of the Solution of Elliptic Problems with Piecewise Analytic Data. II: The Trace Spaces and Application to the Boundary Value Problems with Nonhomogeneous Boundary Conditions

1989 ◽  
Vol 20 (4) ◽  
pp. 763-781 ◽  
Author(s):  
I. Babuška ◽  
B. Q. Guo
Keyword(s):  
Boundary Conditions ◽  
Boundary Value Problems ◽  
Boundary Value ◽  
Elliptic Problems ◽  
Nonhomogeneous Boundary ◽  
Trace Spaces ◽  
Nonhomogeneous Boundary Conditions

scholarly journals Two Legendre-Dual-Petrov-Galerkin Algorithms for Solving the Integrated Forms of High Odd-Order Boundary Value Problems

2014 ◽  
Vol 2014 ◽  
pp. 1-11 ◽  
Author(s):  
Waleed M. Abd-Elhameed ◽  
Eid H. Doha ◽  
Mahmoud A. Bassuony
Keyword(s):  
Boundary Conditions ◽  
Boundary Value Problems ◽  
Boundary Value ◽  
Numerical Algorithms ◽  
Condition Numbers ◽  
Test Functions ◽  
Nonhomogeneous Boundary ◽  
Odd Order ◽  
Nonhomogeneous Boundary Conditions ◽  
The Cost

Two numerical algorithms based on dual-Petrov-Galerkin method are developed for solving the integrated forms of high odd-order boundary value problems (BVPs) governed by homogeneous and nonhomogeneous boundary conditions. Two different choices of trial functions and test functions which satisfy the underlying boundary conditions of the differential equations and the dual boundary conditions are used for this purpose. These choices lead to linear systems with specially structured matrices that can be efficiently inverted, hence greatly reducing the cost. The various matrix systems resulting from these discretizations are carefully investigated, especially their complexities and their condition numbers. Numerical results are given to illustrate the efficiency of the proposed algorithms, and some comparisons with some other methods are made.

scholarly journals Renormalized solutions for some nonlinear nonhomogeneous elliptic problems with Neumann boundary conditions and right hand side measure

2021 ◽  
Vol 39 (6) ◽  
pp. 81-103
Author(s):  
Elhoussine Azroul ◽  
Mohamed Badr Benboubker ◽  
Rachid Bouzyani ◽  
Houssam Chrayteh
Keyword(s):  
Boundary Conditions ◽  
Radon Measure ◽  
Elliptic Problems ◽  
Neumann Boundary ◽  
Neumann Boundary Conditions ◽  
Measure Data ◽  
Renormalized Solutions ◽  
Renormalized Solution ◽  
Nonhomogeneous Boundary ◽  
Nonhomogeneous Boundary Conditions

Our aim in this paper is to study the existence of renormalized solution for a class of nonlinear p(x)-Laplace problems with Neumann nonhomogeneous boundary conditions and diuse Radon measure data which does not charge the sets of zero p(.)-capacity

An inhomogeneous problem for an elastic half-strip: An exact solution

2021 ◽  
pp. 108128652199641
Author(s):  
Mikhail D Kovalenko ◽  
Irina V Menshova ◽  
Alexander P Kerzhaev ◽  
Guangming Yu
Keyword(s):  
Exact Solution ◽  
Boundary Conditions ◽  
Exact Solutions ◽  
Boundary Value Problems ◽  
Boundary Value ◽  
Theory Of Elasticity ◽  
Orthogonality Relation ◽  
Infinite Strip ◽  
Inhomogeneous Problem ◽  
Half Strip

We construct exact solutions of two inhomogeneous boundary value problems in the theory of elasticity for a half-strip with free long sides in the form of series in Papkovich–Fadle eigenfunctions: (a) the half-strip end is free and (b) the half-strip end is firmly clamped. Initially, we construct a solution of the inhomogeneous problem for an infinite strip. Subsequently, the corresponding solutions for a half-strip are added to this solution, whereby the boundary conditions at the end are satisfied. The Papkovich orthogonality relation is used to solve the inhomogeneous problem in a strip.

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